Clerc Marcel G, Verschueren Nicolas
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago Chile.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052916. doi: 10.1103/PhysRevE.88.052916. Epub 2013 Nov 22.
We propose a route to spatiotemporal chaos for one-dimensional stationary patterns, which is a natural extension of the quasiperiodicity route for low-dimensional chaos to extended systems. This route is studied through a universal model of pattern formation. The model exhibits a scenario where stationary patterns become spatiotemporally chaotic through two successive bifurcations. First, the pattern undergoes a subcritical Andronov-Hopf bifurcation leading to an oscillatory pattern. Subsequently, a secondary bifurcation gives rise to an oscillation with an incommensurable frequency with respect to the former one. This last bifurcation is responsible for the spatiotemporally chaotic behavior. The Lyapunov spectrum enables us to identify the complex behavior observed as spatiotemporal chaos, and also from the larger Lyapunov exponents characterize the above instabilities.
我们提出了一种一维稳态模式通向时空混沌的途径，这是低维混沌的准周期途径向扩展系统的自然延伸。通过一个通用的模式形成模型来研究此途径。该模型展示了一种情形，即稳态模式通过两次连续的分岔变得时空混沌。首先，模式经历一次亚临界安德罗诺夫 - 霍普夫分岔，导致出现振荡模式。随后，二次分岔产生相对于前一个频率不可公度的振荡。最后这次分岔导致了时空混沌行为。李雅普诺夫谱使我们能够识别观察到的作为时空混沌的复杂行为，并且还能从较大的李雅普诺夫指数来表征上述不稳定性。
